Abstract

In chapter I a global lunar topographic map is derived from Earth based
and orbital observations supplemented in areas without data by
a linear autocovariance predictor. Of 2592 bins, each 5° square,
1380 (64.7% by area) contain at least one measurement. A spherical
harmonic analysis to degree 12 yields a mean radius of (1737.53 ± 0.03)
km (formal standard error) and an offset of the center of figure of
(1.98 ± 0.06) km toward (19 ± 2)° S, (194 ± 1)° E. A Bouguer gravity
map is also presented. It is confirmed that the low-degree gravity
harmonics are caused primarily by surface height variations and only
secondarily by lateral density variations.

In chapter II a series of models of the lunar interior are derived
from topographic, gravitational, librational and seismic data. The
moon departs from isostasy, even for the low-degree harmonics, with
a maximum superisostatic stress of 200 bars under the major mascon
basins. The mean crustal thicknesses under different physiographic
regions are: mascons, 30-35 km; irregular maria, 50- 60 km; and
highlands, 90-110 km. A significant correlation between lunar surface
chemistry and crustal thickness suggests that regions of thicker crust
are more highly differentiated. A possible mean composition consistent
with our model is an anorthositic crust, underlain by a predominantly
forsterite upper mantle which grades into a refractory rich lower
mantle surrounding a pyrrhotite core.

In chapter III a model of martian global topography is obtained
by fitting a spherical harmonic series of degree 16 to occultation,
radar, spectral and photogrammetric measurements. The existing
observations are supplemented in areas without data by emperical
elevation estimates based on photographic data. The mean radius is
(3389.92 ± 0.04) km . The corresponding mean density is (3.933 ± 0.002)
g cm^(-3). The center of figure is displaced from the center of mass by
(2.50 ± 0.07) km towards (62 ± 3)° S, (272 ± 3)° W. The geometric
Flattening [f_g = (6.12 ± 0 .04) 10^(-3) ] is too great and the dynamic
flattening [f_d (5.22 ± 0 .03) 10^(-3)] is too small for Mars to be
homogeneous and hydrostatic. It is confirmed that, similar to the
Moon, the martian low-degree gravity harmonics are produced primarily
by surface height variations and only secondarily by lateral density
variations. Maps of the global topography and Bouguer gravity are
presented. These are interpreted in terms of a crustal thickness map
which is consistent with gravity, topography and recent preliminary
Viking seismic results. Using plausible density contrasts and an
assumed zero crustal thickness at Hellas, the inferred minimum mean
crustal thickness is (28 ± 4) km.

In chapter IV it is shown that the topographic variance spectra
of the Earth, Moon, Mars and Venus are all very similar. The variance
per harmonic degree V(H;n) decreases roughly as the inverse square of
the degree, or more precisely V(H;n) ≐ V(H;O)/(n)(n+1). On the Earth
and Moon this relationship has been confirmed down to scale lengths as
small as L ≐ 100 m. At the other end of the spectrum, the variance
appears to be deficient relative to this model for scale lengths
greater than L ≐ 2000 km. The most satisfactory explanation for this
phenomenon appears to be a simple equilibrium between constructional
or "tectonic" processes which tend to roughen the surface uniformly
at all scales, and destructional or erosive processes which tend to
smooth the surface preferentially at small scales. The deficiency
in the low-degree variances is attributable to visco-elastic
deformation.